Coordinate-Independent Formulation of Matrix Division
WSEAS TRANSACTIONS ON MATHEMATICS, cilt.25, ss.86-101, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 25
- Basım Tarihi: 2026
- Doi Numarası: 10.37394/23206.2026.25.10
- Dergi Adı: WSEAS TRANSACTIONS ON MATHEMATICS
- Derginin Tarandığı İndeksler: Scopus, INSPEC, zbMATH
- Sayfa Sayıları: ss.86-101
- Karadeniz Teknik Üniversitesi Adresli: Evet
Özet
This paper presents a coordinate-independent formulation of matrix division using the Levi-Civita tensor. It demonstrates that the co-divisor matrix concept, introduced for solving possesses a tensorial structure expressible via the antisymmetric symbol The study provides a proof for the equality between the co-divisor matrix and the classical inverse product, i.e.,
A similar tensor representation is developed for row co-divisors, solving This approach offers a geometrically meaningful framework, enabling a matrix-level generalization of Cramer’s rule and opening new perspectives for solving linear matrix equations.